Lecture Notes in Mathematics
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Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

Authors: Rohde, Christian

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About this book

The main goal of this book is the construction of families of Calabi-Yau 3-manifolds with dense sets of complex multiplication fibers. The new families are determined by combining and generalizing two methods.

Firstly, the method of E. Viehweg and K. Zuo, who have constructed a deformation of the Fermat quintic with a dense set of CM fibers by a tower of cyclic coverings. Using this method, new families of K3 surfaces with dense sets of CM fibers and involutions are obtained.

Secondly, the construction method of the Borcea-Voisin mirror family, which in the case of the author's examples yields families of Calabi-Yau 3-manifolds with dense sets of CM fibers, is also utilized. Moreover fibers with complex multiplication of these new families are also determined.

This book was written for young mathematicians, physicists and also for experts who are interested in complex multiplication and varieties with complex multiplication. The reader is introduced to generic Mumford-Tate groups and Shimura data, which are among the main tools used here. The generic Mumford-Tate groups of families of cyclic covers of the projective line are computed for a broad range of examples.

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Introduction

    Pages 1-9

    Rohde, Jan Christian

  • An Introduction to Hodge Structures and Shimura Varieties

    Pages 11-57

    Rohde, Jan Christian

  • Cyclic Covers of the Projective Line

    Pages 59-69

    Rohde, Jan Christian

  • Some Preliminaries for Families of Cyclic Covers

    Pages 71-78

    Rohde, Jan Christian

  • The Galois Group Decomposition of the Hodge Structure

    Pages 79-89

    Rohde, Jan Christian

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-642-00639-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $59.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1975
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-00639-5
DOI
10.1007/978-3-642-00639-5
Softcover ISBN
978-3-642-00638-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
IX, 228
Topics